Problem: Solve for $x$ and $y$ using elimination. ${5x+3y = 28}$ ${3x+2y = 18}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-2$ and the bottom equation by $3$ ${-10x-6y = -56}$ $9x+6y = 54$ Add the top and bottom equations together. $-x = -2$ $\dfrac{-x}{{-1}} = \dfrac{-2}{{-1}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {5x+3y = 28}\thinspace$ to find $y$ ${5}{(2)}{ + 3y = 28}$ $10+3y = 28$ $10{-10} + 3y = 28{-10}$ $3y = 18$ $\dfrac{3y}{{3}} = \dfrac{18}{{3}}$ ${y = 6}$ You can also plug ${x = 2}$ into $\thinspace {3x+2y = 18}\thinspace$ and get the same answer for $y$ : ${3}{(2)}{ + 2y = 18}$ ${y = 6}$